There is a law governing all natural phenomena. there is no exception to this law - it is exact so far as we know. The law is callled the conservation of energy. it states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. 

Energy has a large number of different forms, and there is a formula for each one. These are: gravitational energy, kinetic energy, heat energy, elastic energy, elastic energy, electrical energy, chemical energy, radiant energy, nuclear energy, mass energy.

Let us consider a pendulum to illusrtate one of the types of Energy. If we pull the ,ass aside and release it. it swings back and forth. In its motion, it loses height in going from either end to the center. Where does the potential energy do?Gravitational energy daisappears when it is  down at the bottom;nevertheless, it will climb up again. the gravitational energy must have gone into another form. Evidently it is by virtue of its motion that it is able to climb up again, so we have the conversion of gravitational energy into some other rofm when it reaches the bottom. 

We can illustrate the existance of energy in other forms by the following example. If we pull down on a spring, we must do some work, for when we have it down, we can lift weight with it. Therefore in its stretched condition it has a possibility of doing some work. elastic energy is the formula for a spring when it stretched.  How much energy is it? If we let gi, the elastic energy, as the spring passes through the equilibrium point, is converted to kinetic energy and it goes back and forth between compressing or stretching the spring. Where is the nergy when  the spring has fifnshed moving up and down? this brings in another form energy: heat energy.

There are ,any other forms of energy but we cannot describe them in any more  detail just now. there is electrical energy, which has to do with pushing and pulling by electric charges. There is radiant energy, the energy of light, which we know is a form of electrical energy of light,, which we know is a form of electrical energy because  light can be represented as wiggilings of the electromagnetic field. There is chemical energy, the energy which is released in chemical  reactions. Actually, electric energy is, to a certain extent, like chemical energy, because chemical energy is the energy of the attraction of the atoms, one for the other, and so is elastic energy. Our modern understanding os the following : chemical energy has two parts, kinetic energy of the electrons inside the aroms, so part of it is kinetic, and electrical energy of interaction of the electrons and the protons- the rest of it, therefore is electrical. Next we come to nuclear energy, the energy which is involved with the arrangement of particles inside the nucleus, and we have the formula for that but we do not have the fundamental laws. We know that it is not electrical. not gravitational, and not purely chemical, but we do not know what it is. it seems to be an additional form of energy.

Finally, associated with the relativity theory, there is a modification of the laws of kinetic energy, so that kinetic energy is combined with another thing called mass energy. An object has energy from its sheer existance. If we have a positron and electron, standing still doing nothing - never mind gravity , never mind anything- and they come together and disappear, radiant energy will be liberated, in a definite amount, and amount can be calculated: All we need know is the mass of the object. It does not depend on what it is - we make two things disappear and we get a certain amount of energy. The formula was first found by Einstein it is  E=mc*2

It is obvious from our discussion that the law of conservation of energy is enormously useful in making analyses and is very important.